Seismometer arrays, first designed and still used to monitor underground nuclear tests, are generally the most sensitive seismological stations, and consequently their reports make a major contribution to earthquake bulletins. The detection of signals at arrays is therefore a foundational field of study in seismology. One of the advantages of arrays over single seismometer stations is that robust statistical criteria can be used to discriminate between real and false detections. Essentially this is because arrays allow the simultaneous estimation of signal and noise power. The F detector, first successfully applied to seismology by Blandford (1974), makes use of this characteristic of arrays. As originally formulated, F requires that the signal be strongly coherent across the array and so is found to be more useful for teleseismic signals than for regional signals. Also the F detector, as originally formulated, requires that seismic noise is uncorrelated between the seismometers in the array. Consequently, at small-aperture (<8 km) arrays, F is often found to be no more useful than traditional detectors based on the ratio of short-term and long-term power averages (STA/LTA) on a beam. Here, the F detector is generalized to make use of a priori information about the signal and noise. This is accomplished by making use of standard least-squares inverse theory, which has been applied to seismometer arrays for over 40 yr. The generalized F detector is then applied to seismograms recorded at the small-aperture (∼3 km) ARCES array in Norway. The enhanced detection capability compared to the traditional F and STA/LTA detectors is demonstrated.